Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#16860797 | C2 | semidirect |
| 3. #30632261 | C2 | semidirect |
| 4. #30632161 | C2 | semidirect |
| 5. #30631905 | C2 | semidirect |
| 6. #30631891 | C2 | semidirect |
| 7. #30631715 | C2 | semidirect |
| 8. #30631681 | C2 | semidirect |
| 9. #419×C251 | C2 | semidirect |
| 18. #22548713 | C22 | semidirect |
| 19. #22548704 | C22 | semidirect |
| 26. Dic251⋊C8 | C22 | semidirect |
| 27. #22548638 | C22 | semidirect |
| 28. #22548635 | C22 | semidirect |
| 32. #103×C251 | C22 | semidirect |
| 116. C251 | #3042 | semidirect |
| 125. #419 | D251 | semidirect |
| 148. #103 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548743 | 2 |
| C22×#16860797 | 2 |
| #30632261 | 2 |
| #30632161 | 2 |
| #30631905 | 2 |
| #30631891 | 2 |
| #30631715 | 2 |
| #30631681 | 2 |
| #419×C251 | 2 |
| #3042 | 251 |